We solve the problem of finding a \((1+\epsilon , (k/\epsilon ))\) -bicriteria solution for the \((k,1)\) -subspace approximation problem on the input \(A(I-P)\) , where \(P\)  is an arbitrary projection matrix onto a subspace of dimension at most \((k/\epsilon )\) , based on techniques from [1]}. We simplify their arguments and obtain tighter parameters for their algorithms. We solve the problem in two stages. First we compute an \((O(1),\tilde{O}(k))\) -approximation, i.e., we find a subspace \(\hat{X}\)  of dimension at most \(\tilde{O}(k)\)  such that
\(\Vert A(I-P)(I-\mathbb {P}_{\hat{X}})\Vert _{1,2} \le O(1)\cdot \textnormal {SubApx}_{k,1}(A(I-P)).\)
